Table 6 Notation used for the Swissmod model
From: The future of Swiss hydropower: how to distribute the risk and the profits?
Indices/sets | Parameters | ||
|---|---|---|---|
\(n \in N\) | Power nodes | mc | Marginal cost |
\(l \in L\) | Power lines | d | Demand |
\(t \in T\) | Time periods (hours) | res | Renewables in-feed |
\({\mathrm{cp}} \in {\mathrm{CP}}\) | Conventional power plants | \({\eta }_{\mathrm{hp}}^{\mathrm{Turb}}\) | Production equivalent [MWh/1000 m3] |
\({\mathrm{hp}} \in {\mathrm{HP}}\) | Hydropower plants | \(\eta _{{{\mathrm{hp}}}}^{{{\mathrm{Pump}}}}\) | Pumping efficiency factor |
\({\mathrm{wn}},\overline{{\mathrm{wn}}},\underline{{\mathrm{wn}}} \in WN\) | Water nodes CH (above, below) | \(\eta _{{{\mathrm{hp}}}}^{{{\mathrm{rt}}}}\) | Pumping round-trip efficiency |
\({\mathrm{co}}\in \mathrm{CO}\) | Countries | inj | Natural inflow to water node [1000 m3] |
Matrices | chp | Combined heat and power | |
\({\mathrm{inc}}_{n,l}\) | Power grid incidence ∈ {0,1, − 1} | \({g}_{\mathrm{cp}}^{\mathrm{max}}\) | Generation capacity |
Variables | \({turb}_{\mathrm{hp}}^{\mathrm{max}}\) | Turbine capacity [MW] | |
G | Electricity generation | \({pump}_{\mathrm{hp}}^{\mathrm{max}}\) | Pump capacity [MW] |
Turb | Discharge (in water for CH, in electricity for EU) | avail | Availability conventional power plants |
Pump | Pumping (in water for CH, in electricity for EU) | \({s}^{\mathrm{max}}\) | Storage capacity [MW for EU, 1000 m3 for CH] |
Cur | Curtailment of renewables | \({\mathrm{{turb}}}_{\mathrm{hp},t}^{\mathrm{profile}}\) | Run-of-river profile (for EU) |
F | Line flow | \({\mathrm{{turb}}}_{\mathrm{hp}}^{year}\) | Dam generation per year (for EU) |
S | Storage level | \({\mathrm{{susceptance}}}_{l}\) | Line susceptance |
WI | Water inflow | voltbase | Line voltage base |
WO | Water outflow | \({f}_{l}^{\mathrm{max}}\) | Line capacity |
Spill | Spillage | securitymargin | Line security margin |
Transfer | Water transferred to other water node (without turbining or pumping) | ||
X | Phase angle difference | ||